Overage Charge or Loyalty Discount: When Should Extra Consumptions Be Penalized or Rewarded?

It is prevalent in many markets that customers are provided menus of tariffs with usage-dependent marginal prices. One instance of such a nonlinear pricing scheme is additional payments on excess consumptions (e.g., overage charge, late fee, and add-on charge for ancillary features or services). Conversely, firms may offer loyalty credit for repeated purchases or consumptions (e.g., quantity discount contracts and redemption points or mileage in reward programs). Interestingly, both increasing and diminishing marginal prices may exist across and within markets but not concurrently on a menu. In this paper, we present a new perspective on whether and when firms should penalize or reward extra consumptions. We consider the standard problem of how a monopoly firm may design a menu of tariffs to sequentially screen consumers with multiple-period consumptions who are heterogenous in consumption value distribution and demand frequency. To relinquish less information rent to the high-type consumers, the optimal design should involve a tariff with increasing (diminishing) marginal price when the demand frequency of the high-value consumers is above or sufficiently lower (slightly lower) than that of the low-value consumers. This general pattern continues to hold under alternative settings on consumer heterogeneity and on uncertainty resolution about multiple-unit demand.